Large coupling-strength expansion of the Møller–Plesset adiabatic connection: From paradigmatic cases to variational expressions for the leading terms

Abstract

and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.• Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal ? Take down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim.

Gradient expansions for the large-coupling strength limit of the Møller-Plesset adiabatic connection

“…The large-λ expansion of the MP AC has recently been uncovered 19,20 for closed-shell systems as follows,…”

“…In other words, the λ → ∞ limit of the MP AC is a crystal of classical electrons bound by minus the Hartree potential generated by the HF density. 19,20 The resulting minimizing positions {r min 1 . .…”

“…r min N } in eq (9), in turn, determine the next leading term, for which eq (7) provides a rigorous variational estimate for closed-shell systems. 20 This term is given by zero-point oscillations around the minimizing positions enhanced by the exchange operator K, which mixes in excited harmonic oscillator states. 20 Finally, the sum in eq (8) only runs over those minimizing positions of eq (9) that happen to be at a nucleus, and it is also a variational estimate.…”

“…20 This term is given by zero-point oscillations around the minimizing positions enhanced by the exchange operator K, which mixes in excited harmonic oscillator states. 20 Finally, the sum in eq (8) only runs over those minimizing positions of eq (9) that happen to be at a nucleus, and it is also a variational estimate. 20 These first three leading terms provide a rigorous framework to link MP perturbation theory with DFT, in terms of functionals of the HF density.…”

“…The λ → ∞ expansion of this MP AC is given by functionals of the Hartree-Fock density ρ HF (r), with a clear physical meaning. 19,20 The strong-coupling functionals of the DFT and the MP AC's are essentially electrostatic energies, whose exact evaluation for large particle numbers is demanding, but while for the DFT AC there are rather accurate second-order gradient expansion approximations (GEA2) 4,7,21 and, more recently, also generalised gradient approximations 16 (GGA), for the MP AC these approximations are not yet available. For this reason, in a very recent work 18 the λ → ∞ functionals of the MP AC have been modeled in an empirical way, starting from the GEA2 of the DFT ones.…”